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Analyzing Neighborhoods of Falsifying Traces in Cyber-Physical Systems.

* Ram Das Diwakaran, Sriram Sankaranarayanan, and Ashutosh Trivedi *

We study the problem of analyzing falsifying traces of cyber-physical
systems. Specifically, given a system model and an input which is a
counterexample to a property of interest, we wish to understand which parts of
the inputs are "responsible" for the counterexample as a whole. Whereas this
problem is well known to be hard to solve precisely, we provide an approach
based on learning from repeated simulations of the system under test.

Our approach generalizes the classic concept of "one-at-a-time" sensitivity
analysis used in the risk and decision analysis commu- nity to understand how
inputs to a system influence a property in question. Specifically, we pose the
problem as one of finding a neighborhood of inputs that contains the falsifying
counterexample in question, such that each point in this neighborhood
corresponds to a falsifying input with a high probability. We use ideas from
sta- tistical hypothesis testing to infer and validate such neighborhoods from
repeated simulations of the system under test. This approach not only helps to
understand the sensitivity of these counterexam- ples to various parts of the
inputs, but also generalizes or widens the given counterexample by returning a
neighborhood of coun- terexamples around it.

We demonstrate our approach on a series of increasingly com- plex examples from
automotive and closed loop medical device domains. We also compare our approach
against related techniques based on regression and machine learning.

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Under review.
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